All bases have an exponent

Math Questions: Laws Of Exponents And Algebraic Fractions

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| By Tjkim

Tjkim

Community Contributor

Quizzes Created: 25 | Total Attempts: 73,672

Questions: 17 | Attempts: 3,537 | Updated: Mar 22, 2023

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Laws of Exponents and Algebraic Fractions

Questions and Answers

1.
- A.
- B.
- C.
Correct Answer
A.
2.
- A.
- B.
- C.
Correct Answer
B.
3.

What is the answer to [(x ⁴ y ⁵)] ⁰

Correct Answer
one
1

Explanation
The given answer "one, 1" suggests that the expression [(x 4 y 5)] 0 evaluates to both the word "one" and the number 1. However, without any context or further information about the expression or the variables x and y, it is not possible to determine the exact meaning or value of the expression. Therefore, the explanation for this answer is not available.

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4
4.

All bases have an exponent
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
When a base has no exponent written it is assumed to be 1, thus all bases have an exponent even if none is written.

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6
1
5.

The result of simplifying the expression (x ³ y ⁴ ) ³ is
- A.
- B.
- C.
  
  Y
Correct Answer
A.

Explanation
Multiply the power of x by 3 from the outside of the expression to get x^9. Multiply the power of y by 3 from the outside to get y^12

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6.

x ⁴ x ³ will result in an exponent of

Correct Answer
7
seven

Explanation
The expression "x 4 x 3" can be simplified as "x^4 * x^3". When multiplying two powers with the same base, you add the exponents. In this case, the base is "x" and the exponents are 4 and 3. So, the sum of the exponents is 7, resulting in an exponent of 7 for the expression.

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2
4 4
7.

A³ x a² =
- A.
- B.
  
  A
- C.
Correct Answer
C.
8.

Ac⁴ x a³c² =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression "ac4 x a3c2" represents the multiplication of the terms "ac4" and "a3c2". In this expression, "ac4" means "a" multiplied by "c" multiplied by 4, and "a3c2" means "a" multiplied by 3 multiplied by "c" squared. To multiply these terms, we can multiply the coefficients (4 and 3) together to get 12, and multiply the variables (a and c) together to get "a" multiplied by "c". Therefore, the result of the expression is 12ac.

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2
3
9.

4a³ x 3a⁵ =
- A.
- B.
- C.
Correct Answer
C.

Explanation
The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables. Therefore, 4a3 x 3a5 is equal to 12a8.

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3
0
10.
- A.
- B.
- C.
Correct Answer
A.
11.
- A.
  
  3a
- B.
- C.
Correct Answer
C.
12.
- A.
- B.
- C.
Correct Answer
B.
13.

(a⁴)⁶ =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression (a4)6 can be simplified by multiplying the two numbers within the parentheses first. Since there is no variable or operation between the parentheses and the number 4, we can assume that it is a multiplication operation. Therefore, (a4)6 is equivalent to 4 * 6, which is 24.

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14.

(2a³c⁵)³ =
- A.
- B.
- C.
Correct Answer
C.
15.
- A.
- B.
- C.
Correct Answer
A.
16.
- A.
- B.
  
  A
- C.
  
  C
Correct Answer
A.
17.

(3a⁴)² =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression, (3a4)2, can be simplified by first evaluating the exponent, which is 2. This means that the expression inside the parentheses, 3a4, needs to be squared. To square this expression, we multiply it by itself. So, (3a4)2 = (3a4) x (3a4) = 9a8.

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0
1